Question: $\int x^{^{\frac14}}\,dx=$ $+C$
The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int x^{^{{\frac14}}}\,dx&=\dfrac{x^{^{{\frac14}+1}}}{{\dfrac14}+1}+C \\\\ &=\dfrac45x^{^{\frac54}}+C \end{aligned}$ In conclusion, $\int x^{^{\frac14}}\,dx=\dfrac45x^{^{\frac54}}+C$